2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | Q.3.5 | ||
| Paper Title | Classical Coding Problem from Transversal T Gates | ||
| Authors | Narayanan Rengaswamy, Robert Calderbank, Michael Newman, Henry D. Pfister, Duke University, United States | ||
| Session | Q.3: Quantum Error Correcting Codes and Decoding | ||
| Presentation | Lecture | ||
| Track | Quantum Systems, Codes, and Information | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical T and T^{-1} gates. For example, this could enable magic state distillation with non-CSS codes and, thus, provide better parameters than CSS-based protocols. However, among non-degenerate stabilizer codes that support transversal T, we prove that CSS codes are optimal. We also show that triorthogonal codes are, essentially, the only family of CSS codes that realize logical transversal T via physical transversal T. Using our algebraic approach, we reveal new purely-classical coding problems that are intimately related to the realization of logical operations via transversal T. Decreasing monomial codes are also used to construct a code that realizes logical CCZ. Finally, we use Ax's theorem to characterize the logical operation realized on a family of quantum Reed-Muller codes. This result is generalized to finer angle Z-rotations in https://arxiv.org/abs/1910.09333. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
